A request qubit is stored in some noisy memory when waiting for an EPR pair. If more requests arrive while one is already in memory, a queue is formed. As stated previously, this allows us to model the memory platform as a CTMC allowing for the calculation of wait time distributions. To quantify the effects of decoherence, we need a continuous time noise model that captures information loss. We choose the dephasing or the phase damping model[1]} represented by the operator \(\varepsilon (\rho )\) , where \(\rho \)  is some density matrix of a one qubit system. It is mathematically defined as
\(\varepsilon \left(\begin{bmatrix} \rho _{00}& \rho _{01}\\ \rho _{10}& \rho _{11} \end{bmatrix} \right)=\begin{bmatrix} \rho _{00}& e^{-\Gamma t}\rho _{01}\\ e^{-\Gamma t}\rho _{10}& \rho _{11} \end{bmatrix}\) 
